{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "ac2c0891",
   "metadata": {},
   "source": [
    "# Integrating arbitrary ODEs\n",
    "\n",
    "Although REBOUND is primarily an N-body integrator, it can also integrate arbitrary ordinary differential equations (ODEs). Even better: it can integrate arbitrary ODEs in parallel with an N-body simulation. This allows you to couple various physical effects such as spin and tides to orbital dynamics.\n",
    "\n",
    "In this example, we are integrating a two planet system and a decoupled harmonic oscillator which is governed by the following ODE:\n",
    "\n",
    "$$ y_0(t)'' = -\\frac km y_0(t)$$\n",
    "\n",
    "or equivalently as a set of 2 first order differential equations\n",
    "\n",
    "$$         \\begin{pmatrix} y_0(t)\\\\y_1(t)\\end{pmatrix}' =  \\begin{pmatrix} y_1(t)\\\\- \\frac k m y_0(t)\\end{pmatrix}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "e350dbbb",
   "metadata": {},
   "outputs": [],
   "source": [
    "import rebound\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "37ac5371",
   "metadata": {},
   "source": [
    "We first set up our N-body simulation. Note that we are using the Gragg-Bulirsch-Stoer integrator (BS)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "18043d1d",
   "metadata": {},
   "outputs": [],
   "source": [
    "sim = rebound.Simulation()\n",
    "sim.add(m=1)\n",
    "sim.add(a=1.2,m=1e-3,e=0.1)\n",
    "sim.add(a=2.3,m=1e-3,e=0.1)\n",
    "sim.integrator = \"BS\""
   ]
  },
  {
   "cell_type": "markdown",
   "id": "55150ae8",
   "metadata": {},
   "source": [
    "We now create an ODE structure. Note that the ODE is linked to the simulation. If you run multiple simulations in parallel, you need to create an ode structure for each of them."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "39c5337d",
   "metadata": {},
   "outputs": [],
   "source": [
    "ode_ho = sim.create_ode(length=2, needs_nbody=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f5766f9e",
   "metadata": {},
   "source": [
    "Next, we setup the ODE structure with the initial conditions and the right hand side (RHS) of the harmonic oscillator:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "265f8c39",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Mass and spring constants\n",
    "m = 1.\n",
    "k = 10.\n",
    "\n",
    "# Initial conditions\n",
    "ode_ho.y[0] = 1. \n",
    "ode_ho.y[1] = 0. # zero velocity\n",
    "\n",
    "# RHS\n",
    "def derivatives_ho(ode, yDot, y, t):\n",
    "    yDot[0] = y[1]\n",
    "    yDot[1] = -k/m*y[0]\n",
    "\n",
    "ode_ho.derivatives = derivatives_ho    "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2f9b90c7",
   "metadata": {},
   "source": [
    "To keep track of how accurate the integration of the harmonic oscillator is, we can calculate the energy which is conserved in the physical system."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "ebc52cd3",
   "metadata": {},
   "outputs": [],
   "source": [
    "def energy_ho(ode):\n",
    "    return 0.5*k*ode.y[0]**2 + 0.5*m*ode.y[1]**2"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6bff9751",
   "metadata": {},
   "source": [
    "Now we can run the simulation, keeping track of a few quantities along the way."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "4eb25927",
   "metadata": {},
   "outputs": [],
   "source": [
    "times = np.linspace(0.,60.,1000)\n",
    "energies_nbody = np.zeros(len(times))\n",
    "energies_ho = np.zeros(len(times))\n",
    "r_nbody = np.zeros(len(times))\n",
    "x_ho = np.zeros(len(times))\n",
    "\n",
    "for i, t in enumerate(times):\n",
    "    sim.integrate(t)\n",
    "    \n",
    "    r_nbody[i] = sim.particles[1].d\n",
    "    x_ho[i] = ode_ho.y[0]\n",
    "    energies_nbody[i] = sim.energy()\n",
    "    energies_ho[i] = energy_ho(ode_ho)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "439539a6",
   "metadata": {},
   "source": [
    "Let's plot the relative energy error over time for both the N-body and the harmonic oscillator integration."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "0411c827",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x107fc2c10>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1,1)\n",
    "ax.set_xlabel(\"time\")\n",
    "ax.set_ylabel(\"relative energy error\")\n",
    "ax.set_yscale(\"log\")\n",
    "ax.plot(times,np.abs((energies_nbody-energies_nbody[0])/energies_nbody[0]), label=\"N-body\")\n",
    "ax.plot(times,np.abs((energies_ho-energies_ho[0])/energies_ho[0]), label=\"harmonic oscillator\")\n",
    "ax.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6421232c",
   "metadata": {},
   "source": [
    "Let us also plot the radius of the inner planet and the position coordinate of the harmonic oscillator."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "bf8928b4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1122a4df0>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1,1)\n",
    "ax.set_xlabel(\"time\")\n",
    "ax.plot(times,r_nbody, label=\"planet\")\n",
    "ax.plot(times,x_ho, label=\"harmonic oscillator\")\n",
    "ax.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2ef6fafa",
   "metadata": {},
   "source": [
    "The above example is using the BS integrator for both the N-body and the harmonic oscillator integration. The BS integrator has default tolerance parameters set to $10^{-5}$. You can change the relative or absolute tolerance with to get more accurate results:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "1d3c7ced",
   "metadata": {},
   "outputs": [],
   "source": [
    "sim.ri_bs.eps_rel = 1e-8\n",
    "sim.ri_bs.eps_abs = 1e-8"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1e2b0d95",
   "metadata": {},
   "source": [
    "Note that in this example, the harmonic oscillator has a period that is shorter than any orbital timescale. Therefore the timestep is limited by the harmonic oscillator, not the N-body integration. As a result, the N-body integration has an error much smaller than the tolerance parameters.  "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9bb09a10",
   "metadata": {},
   "source": [
    "Let us change the simple harmonic oscillator to a forced harmonic oscillator where the forcing depends on phase of a planet."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "03c94568",
   "metadata": {},
   "outputs": [],
   "source": [
    "def derivatives_ho_forced(ode, yDot, y, t):\n",
    "    # Now we can access particles and their orbital parameters during sub-steps\n",
    "    forcing = np.sin(sim.particles[1].f)\n",
    "    \n",
    "    # Note that we are using the global sim variable.\n",
    "    # Alternatively, one can also access the simulation via\n",
    "    # sim = ode.contents.r.contents \n",
    "    \n",
    "    yDot[0] = y[1]\n",
    "    yDot[1] = -k/m*y[0] + forcing\n",
    "\n",
    "ode_ho.derivatives = derivatives_ho_forced"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c592c246",
   "metadata": {},
   "source": [
    "We explicitly set `needs_nbody = False` during initialization. We therefore need to tell REBOUND that our ODE now needs access to the particle state during the integrations:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "61034468",
   "metadata": {},
   "outputs": [],
   "source": [
    "ode_ho.needs_nbody = True"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3dfafc1d",
   "metadata": {},
   "source": [
    "Running the integration a bit further, now with the forced harmonic oscillator:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "4305edc4",
   "metadata": {},
   "outputs": [],
   "source": [
    "times = np.linspace(65.,120.,1000)\n",
    "\n",
    "for i, t in enumerate(times):\n",
    "    sim.integrate(t)\n",
    "    \n",
    "    r_nbody[i] = sim.particles[1].d\n",
    "    x_ho[i] = ode_ho.y[0]\n",
    "    energies_nbody[i] = sim.energy()\n",
    "    energies_ho[i] = energy_ho(ode_ho)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "191064cf",
   "metadata": {},
   "source": [
    "The harmonic oscillator is now getting forced by the planet."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "9f90e0fb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1122f46a0>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1,1)\n",
    "ax.set_xlabel(\"time\")\n",
    "ax.plot(times,r_nbody, label=\"planet\")\n",
    "ax.plot(times,x_ho, label=\"harmonic oscillator\")\n",
    "ax.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "80beed0f",
   "metadata": {},
   "source": [
    "In addition to using BS, it is also possible to integrate arbitrary ODEs in conjunction with other REBOUND integrators such as IAS15 and WHFast. In that case, only the user-defined ODEs are integrated with BS **after** a successfull N-body integration step. This type of switching back and forth the different ODEs will lead to an error. However, if the timescale involved in the user-defined ODEs are much longer than the timestep of the N-body integration, then this will be a small error. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "15c2b8e3",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
